Algorithm for processing the results of calculations for determining the body of optimal parameters in the weighted finite element method
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 15 (2022) no. 4, pp. 71-79
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The weighted finite element method allows to find an approximate solution to a boundary value problem with a singularity faster in $10^{6}$ times than the classical finite element method for a given error equal to $10^{-3}$. In this case, it is required to apply the necessary control parameters in the weighted finite element method. The body of optimal parameters is determined on the basis of carrying out and analysing a series of numerical experiments. In this paper we propose an algorithm for processing the results of calculations and determining the body of optimal parameters for the Dirichlet problem and the Lamé system in a domain with one reentrant corner on the boundary taking values from $\pi$ to $2\pi$.
Keywords:
corner singularity, weighted finite element method, body of optimal parameters.
@article{VYURU_2022_15_4_a5,
author = {V. A. Rukavishnikov and D. S. Seleznev and A. A. Guseinov},
title = {Algorithm for processing the results of calculations for determining the body of optimal parameters in the weighted finite element method},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {71--79},
publisher = {mathdoc},
volume = {15},
number = {4},
year = {2022},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VYURU_2022_15_4_a5/}
}
TY - JOUR AU - V. A. Rukavishnikov AU - D. S. Seleznev AU - A. A. Guseinov TI - Algorithm for processing the results of calculations for determining the body of optimal parameters in the weighted finite element method JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2022 SP - 71 EP - 79 VL - 15 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURU_2022_15_4_a5/ LA - en ID - VYURU_2022_15_4_a5 ER -
%0 Journal Article %A V. A. Rukavishnikov %A D. S. Seleznev %A A. A. Guseinov %T Algorithm for processing the results of calculations for determining the body of optimal parameters in the weighted finite element method %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2022 %P 71-79 %V 15 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2022_15_4_a5/ %G en %F VYURU_2022_15_4_a5
V. A. Rukavishnikov; D. S. Seleznev; A. A. Guseinov. Algorithm for processing the results of calculations for determining the body of optimal parameters in the weighted finite element method. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 15 (2022) no. 4, pp. 71-79. http://geodesic.mathdoc.fr/item/VYURU_2022_15_4_a5/